England & Wales demography by age, 2010-2021

Any analysis of the mortality of covid depends on comparing the death rate with that of other years. A direct comparison is unfair because the population of 2020-2021 is larger than in earlier years and has a greater proportion of older people. This post produces age distribution date for the years 2010-2021, stating the sources and explaining the method by which the age distributions are calculated.

2011 census figures
2011 census has detailed figures of the Usual resident population by five-year age group for the whole of the UK and England and Wales figures alone.

These figures show that, in each age group, the population of Scotland and Northern Ireland are an average of 11.24% of the population of the whole of the UK, a figure comparable with that used in previous calculations of the England and Wales population compared with that of the UK as a whole.

2018 estimated population figures
2018 figures are projections calculated by ONS. These projections give projected numbers in 1-year wide age ranges, from which the five-year age groups can be calculated.

Filling in the over-80 figures
The 2011 census lumps together all the over-80 figures. For the purposes of more detailed analysis, five-year age groups for over-80s have been constructed, distributing the 2011 figures for over-80s amongst the five-year age groups, assuming that the (reduced) number of over-80’s is distributed over the upper years in 2011 in the same way that the (larger) number of over-80’s in 2018 is distributed.

The above sources and calculations give us these figures:

From this we get the following population distributions for 2011 and 2018.

Note how the columns for 2018 are distinctly taller than 2011 in the age group above 50 as the bulges in the 40-49 group have aged between those two years and moved from their fifties to their sixties.

If we compare the population numbers in each age group between the two years 2011 and 2018, we see that the numbers over 65 are very significantly higher in 2018 because the effect already seen (an aging population) combines with an increasing population. Both of these effects lead to higher expected death rates.

Dishwashing, hand vs machine

What are the costs of dishwashing and the relative costs of machine vs hand dishwashing?

Hand washing
A typical bowl has a capacity of approximately 12 litres when full. Suppose that one fills it to 10 litres and then, in the process of rinsing, replacing, topping up, etc, one uses twice that amount, ie 20 litres, which has a mass of 20 kg.

This water has to be bought and there is a charge for disposing of it. If both supply and sewerage are metered, these are in the order of £1.50 per cubic metre for both supply and sewerage, ie a total of £3 per cubic metre or £3/1000 = 0.3 p/litre. So the 20 litres of water cost 20 x 0.3p = 6p.

That water has to be heated, from an average temperature of 10°C to around 50°C. That is a rise of 40 K. (The kelvin, symbol K, is the unit of temperature difference, but you could, perfectly adequately, say that it was a rise of 40 °C.)

The energy needed to raise 20 kg of water by 40 K is
20 kg x 4200 J/kg K x 40 K = 3,360,000 joules = 3.36 megajoules (MJ). (4200 J/kg K is the specific heat capacity of water, the energy needed to raise the temperature of 1 kg of water by 1 K.)

The standard unit of energy supply is the kilowatt-hour (kWh), which is 3.6 MJ. So the energy needed to raise 20 kg of water to 50°C for washing up is 3.36/3.6 = 0.93 kWh.

If one heats the water by full-rate electricity, at 17 p/kWh, the heating of the water costs 0.93 x 17p = 15.8p.

If one heats the water by off-peak electricity at 10 p/kWh, the cost is 0.93 kWh x 10p/kWh = 9.3 p.

If one heats the water by gas, when gas costs 3 p per kWh, the cost of doing that depends on the efficiency of the water heating process. Typically gas water heating is 50% efficient, meaning that the heating actually costs 6 p per kWh. So for 0.93 kWh, the cost is 0.93 x 6p = 5.6p.

Washing up liquid
A modest squirt of washing up liquid is about 8 g. If the washing up requires 4 squirts, that is a total of 32 g, about 32 ml.

Tesco Lemon washing up liquid (Aldi price match they say) costs 73p/litre. So 32 ml costs (32/1000) x 73p = 2.3p.

So hand washing our significant load of dishes costs:
water supply and disposal – 6p
heating the water – 9p (using the middle calculated value above)
washing-up liquid – 5p (I’ve allowed for a number of extra squirts)
Total – 20p/wash

Machine dishwashing
Let’s compare this with using a dishwasher.

The Hotpoint HFE 1B19 has an energy rating of A+. It uses 12 litres of water per cycle and an energy consumption of 1.039 kWh.

The water costs are 12 litres x 0.3p/litre = 3.6p.

The energy costs for the water are 1.039 kWh x 17 p/kWh = 17.6p. This is significant more than that for the hand washing because, unless the dishwasher is run overnight, it heats the water on full-price electricity and neither on off-peak electricity, nor gas.

Tesco All-in-one lemon dishwasher tablets are £3 for 30 tablets, so 10p/tablet.

This Hotpoint dishwasher costs £270. If it does 1 wash per day for 5 years that’s 365 washes per year x 5 years = 1825 washes. The capital cost of the machine per wash is £270/1825 = 14 p/wash.

So the cost of machine dishwashing is:

water supply and disposal – 4p
heating the water – 18p
dishwasher tablet – 10p
capital cost of machine – 14p
Total – 46p

Our dishwasher may last more than 5 years with 1 wash per day. So perhaps the capital cost may be down to 10 p per wash. That brings the cost per dishwasher cycle down to 42 p. Our handwashing may actually use 4 bowls’-worth of water, doubling the cost to 40p. That makes cost per hand wash 40 p per wash, compared with the machine wash cost of 42p.

Even if most of the dishes are washed in the machine, there are usually some items that need hand washing. A comparison between hand washing and dishwashing needs to take into account that machine dishwashing is usually accompanied by some hand washing.

There isn’t really much to choose between hand and machine dishwashing. They are of similar cost but the indications are that machine dishwashing is possibly somewhat more expensive.
Dishwashing costs in the order of 40p per big load, perhaps 40p x 365 = £146 per year. Let’s call that £150 per year.
Energy costs are about 40% of that, around £60 per year.

Diesel and petrol costs compared with other fuels

Before comparing running costs of different types of car, it is worth thinking about the cost of petrol and diesel compared with electricity and indeed other fuels. This post is the first part of a series. We begin by considering the raw costs of fuel. Next we consider the efficiency with which we can use those fuels, which affects the real costs of use. The third part looks how taxes affect the real costs.

Before making a comparison, it’s useful to remind ourselves of the units we are using. Lift an apple (100g) up a metre and you’ve done about a joule of work. Do that 3.6 million times and you’ve done 3,600,000 joules of work: that’s 1 kilowatt hour (kWh), the standard unit for supplying gas and electricity to the home.

Here is a direct comparison of the costs to the consumer of electricity, petrol and diesel.

We are comparing all the fuels by the price per kilowatt-hour, even though we don’t buy petrol and diesel by the kilowatt-hour.

What is there to remark on? Perhaps that the different fuel costs per kWh are broadly similar and there is no obvious reason, from this information, leading us to think that electric cars should be cheap to run.

We buy petrol and diesel in litres rather than kWh and we know that diesel fuel is significantly more expensive than petrol. Yet the cost per kilowatt-hour for the two fuels is similar. It’s not hard to see that diesel fuel contains more energy per litre.

Let’s follow the numbers.

A litre of petrol has an energy content 9.4 kWh per litre and petrol currently costs 116.4p per litre. So the price per kWh is 116.4/9.4 = 12.4p per kWh.

A litre of diesel has an energy content of 10.3 kWh and costs 120.6p. So the price per kWh is 120.6/10.3 = 11.7p per kWh. We can see one reason why diesel cars cheaper to run than petrol cars: diesel, despite being 4% more expensive, is about 6% cheaper per kWh.

Buying electricity from the electricity supply at home, we pay about 17 p per kWh. Some electricity tariffs supply electricity more cheaply at night and charge a bit more per day (20p) and less (10p) for the 7 hours overnight, averaging the same 17p per kWh.

Public electric charging stations
Electric cars are in their infancy. Charging at home is a recent step. But public charging stations are even more of an innovation. The prices of the services they provide will no doubt change over time but at the moment it can be much more expensive to charge your car from a station ‘on the road’. Ionity fast chargers charge 69p per kWh, with other providers charging more than twice what you would pay at home. If these costs become applied generally, electricity will certainly not be a cheap fuel. On the other hand Lidl charges 23p p/kWh at the moment, a reasonable mark-up for the cost of providing the service. Tesco is free but one can’t see that lasting.

You can stop here if you like
The rest of this post is concerned with following the numbers through for a wide variety of fuels, not all of them for transport. I’ve put these figures here because I think it’s fun to collate all the fuel information and also so that later on I can branch off into considering domestic heating. You might like to have a quick look at the summary table a bit further down before departing.

Road LPG
LPG stands for liquefied petroleum gas, It liquefies under modest pressures and so can be stored in tanks and used for domestic and commercial heating and for vehicle propulsion.
LPG has an energy content of 7.2 kWh per litre and at a current price of about 65p per litre, that’s 65/7.2 = 9p per kWh.

Heating LPG
Here we find our first consideration of the effect of tax on prices. LPG for heating has much less tax on it than LPG for transport. That brings its costs down to a typical 36 p per litre and with the energy stored being 7.2 kWh/litre, that equates to 36/7.2 = 5 p per kWh.

Red Diesel
Red diesel is a tax-free version of road diesel, used for purposes like powering agricultural vehicles or heating. It is ordinary road diesel that has a red dye to colour it to check it is not used for taxable purposes. Red diesel has the same energy content as road diesel at 10.3 kWh per litre but the reduced tax means that it costs only about 60p per litre. So the price per kWh is 60/10.3 = 5.8p per kWh.

(Natural) Gas
Gas costs about 3p per kWh at the moment. That’s because the oil price is very low due to the covid crisis. My own view, for reasons that I might address eventually, is that the ‘right’ price for gas is 5p per kWh.

Summary of fuel costs
I’ve decided to summarise the fuel costs at this point before you get too bored with repeated calculations. The remaining calculations and some comments on the fuels follow the table.

Heating oil
10.85 kWh per litre and 41p per litre, which gives 41/10.85 = 3.8p per kWh.

Solid fuel
House Coal is £267 per tonne (1000 kg) or 26.7p per kg. Its calorific value is about 7 kWh/kg. So the cost per kWh is 26.7/7 = 3.8p per kWh.
Anthracite is 40p/kg with a calorific value of 9.2 kWh/kg, giving a cost of 40/9.2 = 4.34 p/kWh.
Blaze Smokeless house fuel is 33.5 p/kg, with a calorific value of 5 kWh/kg giving a cost of 33.5/5 = 6.7 p/kWh.
Like all fuels in which there is direct negotiation with the supplier, solid fuels prices depend on your ability to haggle and the time of the year at which you are buying. You can buy smokeless fuel for 28p/kg in the summer, much less than its winter price.

Wood pellets
£265 for 1150 kg, which is 23p/kg. Calorific value around 4.9 kWh/kg, which gives 23/4.9 = 4.7 p/kWh.
My own view is that wood pellets are not, in general, a renewable source of energy. Wood sawdust should be used to make materials like MDF (medium density fibreboard) which is used instead of wood in many products. Those who use them believing that the have some benefit in ‘saving the planet’ should think twice. Burning pellets of wood results in more living trees being cut down and therefore encourages the destruction of the natural environment.

Kiln dried Ash logs, £350 for 750 kg = 47p/kg. Calorific value 5.5 kWh/kg, giving 47/5.5 = 8.5 p/kWh.

Manufactured heat logs
Wickes; £6.50 for 9.5 kg, a pack of 12. That’s 68p/kg. There is no given figure for the calorific value of this product but the forest research reference below indicates that the calorific values of all woods is about 5 kWh/kg. So these Heat Logs cost 68/5 = 13.7 p/kWh. They are an expensive form of heating, particularly when we take into account efficiency in the next post on this subject.

Sources of information
Figures for this post date from January 2020

Lost poem – Elgar

This poem, about Elgar, is a memory from childhood. It’s quirky and amusing.

I’ve googled it, etc, with no luck. So I stick it here wondering if a search engine will pick it up and a fellow seeker will find that he isn’t a lone seeker.

Try to imagine if you can
That Elgar was a handyman,
And when not writing tunes and airs
Was very fond of making chairs,
And he derived such merriment
From chemical experiment.

Another thing you’d often see
Was Elgar chopping down a tree,
And once he made a double bass
Out of an ancient packing case.
I think this fact sticks out a mile:
Elgar was very versatile.

Hot water timing – a waste of effort.

It goes against our nature to be told there is nothing one can do about something but sometimes logic drives us to that conclusion. Energy saving heating controls are sometimes like that. Some controls are worthwhile: others are not. Despite apparently well-qualified sources saying the contrary, if one has a modern hot water cylinder heated by oil or gas, it saves almost no energy to have the hot water timed, rather than have it turned on continuously.

Here is the energy label from typical recent hot water cylinder.

This label shows that the cylinder has a volume of 150 litres and loses heat at the rate of 60 watts (60 joules per second).

Calculating the energy loss
Losing energy at 60 joules per second means 60 x 3600 = 216,000 J per hour.
Overnight (from 10 pm to 6 am) or during the day (from 8am to 4 pm) are 8-hour stretchs, so during that time the total energy loss is 8 x 216,000 joules = 1,728,000 joules = 1.78 MJ. That’s 1.78/3.6 kWh, about half a kilowatt hour, ie about 3 p if you heat your hot water by gas.

So, every morning, or every evening, if the hot water has been turned off for 8 hours, the boiler uses 3 p worth of fuel just to top up the losses during the day. That’s 6 p per day, or £22 per year. Is there the possibility of saving some of that energy wasted?

As the tank loses energy it cools down
The tank contents are 150 litres (150 kg) of water. We can calculate how much its temperature falls.
Energy = mass x specific heat capacity x temperature change.
1,728,000 joules = 150 kg x 4200 J/kg K x temperature change
temperature change = (1,728,000)/(150 x 4200) = 2.74 °C (Physicists label that 2.47 K)

If the hot water is turned off, the temperature drops a small amount.
If your controls turn the hot water off for an 8-hour period, your hot water drops in temperature by about 3 °C, say from a set temperature of 65 °C down to 62 °C. That means its average temperature is 63.5 °C.
The first effect of the heating system when the time turns the hot water system back on is to heat the water back up to 65 °C. That’s where the 3 p worth of energy is used.

If the hot water is left on, the temperature doesn’t fall
If you leave your heating switched on, the hot water stays at 65 °C. Whenever the thermostat senses that the temperature dropping, it turns the heating system on to top it back up. So instead of having to reheat the water when the system turns back on, it is continually topping up the energy loss – by an amount pretty much the same as the 3-p-worth which it needs if it switches the hot water off.

But surely you save some energy by turning off?
If you keep the hot water on, it is at a steady 65 °C, that is steadily 45 °C above the 20 °C surrounding room.
If your controls turn the hot water off for an 8-hour period, the tank temperature drops from 65 °C down to 62 °C, an average of 43.5 °C above the surroundings. This is not very different from leaving the hot water on and therefore the heat loss is pretty similar.

If, when switched off, the temperature above the surroundings has dropped in the proportion 43.5/45 compared with leaving the hot water turned on. The energy loss, and the cost of the energy loss, has dropped in the same proportions.

So the heat losses during switched-off times go from £22 a year to = £22 x 43.5/45 = £21.27 a year. That means that the reheating costs drop by 83p a year.

If you have oil or gas central heating and you control your hot water heating and turn it off for periods during the day, you might save £1 a year, a trivial saving against the convenience of hot water at any time or the simplifications of your heating control system.

In fact the savings are even less
So far we’ve assumed that all the ‘losses’ from the hot water cylinder are waste. This is not always the case. At times of year when a house is being heated, energy ‘lost’ from the boiler is useful in heating the house. If the house is being heated by gas, a 60 W loss from the hot water tank is worth as much as about a 20 W heating from the gas boiler during the heating season, so the potential savings of switching off drop to about 70p a year. If you are heating by on-peak electricity, the 60 W ‘lost’ is just as good as 60 W produced by your electrical heating, so the savings are about 42 p per year.

What about longer periods of switch-off
If you are away for a whole 24-hour day, that’s three times as long as the 8-hour periods we’ve considered. If you turned the heating off for that day away, the hot water temperature would drop by about 3 x 2.47 K, = 7.4 K, ie down from 65 °C to 57.6 °C, an average temperature of 61.3 °C, ie 41.3 K above the surroundings. This would take the heat loss down to 8.3p. So you can save 0.7 p by turning off the heating if you are aware for a day. Only if you are away for several days during which the tank temperature will drop very significantly, is it worth turning the hot water off. If you turn the tank off when you are away for a week, you will save about 60p. With the average household away for less than 4 weeks a year, turning off hot water when one is away can save at the most a couple of pounds a year.

If you have a combi boiler
Most combi boilers heat hot water on demand. With them there is no stored hot water and no ability to turn the hot water off. Some combi boilers have a small reservoir of water that is always kept hot so that the boiler delivers hot water even more quickly. One can save a small amount of energy by turning this pre-heat system off but manufacturers do not recommend it because the savings are small.

The only time is is worth controlling hot water heating
If you have off-peak water heating it is worth controlling the hot water heating. In that situation it makes sense to make sure that the heating of the hot water is done during the night. Let’s run the calculations.

In a flat occupied by 2 people, hot water consumption might be 100 litres (100 kg) of water per day. This water has to be heated from an average temperature of 10 °C to, 65 °C, an increase of 55 kelvin. The energy needed to heat this water is
mass x specific heat capacity x temperature rise
= 100 kg x 4200 joule/kg K x 45 K = 18.9 MJ = 18.9/3.6 = 5.25 kWh.

Heating this by on-peak electricity at 14.9p per kWh costs 14.9 x 5.25 = 78 p per day.

Heating this by off-peak electricity at 9.3 p per kWh costs 9.3 x 5.25 = 49 p per day.

So you can save 29 p per day, ie £106 per year, by using off-peak electricity.

Under those circumstances only is it worth controlling the time at which you heat the water.

Topping-up electrically heated hot water
Many electrically heated hot-water systems have a top-up facility by which one can turn an immersion heater on if one runs out of off-peak-heated water.

If one needs the top-up regularly, then certainly one is using more than 100 litres per day and there is value in considering a larger tank. There are savings in the order of £200 per year if one heats 200 litres of water a day with off-peak electricity rather than with on-peak.

On the other hand, if one tops up rarely, the easiest thing to do is to set the overnight heater to a high temperature and the top-heater to a lower temperature. It will rarely turn itself on and the cost of having hot water always available will be less than £10 a year if one found that one was turning the on-peak heater on less often than once a week.

There are exceptions to this analysis. If one wears hair shirts and likes to be nagged into reduced water consumption, rely on the overnight hot water running out and giving you the occasional cold shower so that you have less time in the shower and take pleasure in using less hot water and less energy.

In practice there are a number of confusing factors to this analysis. Experience shows that those households in which saving energy is a high priority are also those with drench showers that use most water…

Other reasons for switching the hot water off at night.
Sometimes the most numerate don’t like the feeling that there is nothing that one can do to effect a significant saving and they want to control the water heating whatever. Sometimes there is a light sleeper in the house disturbed by the noise of the hot water system…

Surely there is something you can do?
Modern hot water cylinders are much more effectively insulated. If your hot water cylinder is old, and by that I mean perhaps as little as 10 years old because insulation standards have increased rapidly in the last decade, it is worth considering a new hot water cylinder.

Hot water cylinder swap worthwhile?
Heat your hot water cylinder fully and measure the hot water temperature (say at the tap with a cooking thermometer). Then turn off its heating completely and measure the hot water temperature after 8 hours.
If the temperature falls by less than 5 °C in eight hours your cylinder is well-enough insulated. The greater fall than this, the more worthwhile it is swapping the cylinder. If the temperature falls by 20 °C in 8 hours, you’ll save well over a hundred pounds a year by upgrading to a modern hot water cylinder.

The green serenity prayer
As always it makes sense to change the things that matter, accept the things that don’t and have the wisdom to know the difference.

Electric cars 1 – baseline figures: electric cars vs an economical diesel

Small electric cars
Carwow recently tested 6 small electric cars. They were able to travel between 3.7 and 5.2 miles per kWh and had ranges between 113 and 229 miles. That’s a factor of 2 in the range but the battery sizes varied from 28.5 kWh to 52 kWh. Roughly, if you have twice the battery size, you can go twice as far. The best was the Renault Zoe which, with the 52 kWh battery, has a mass of about 1500 kg, or a ton and a half.

Larger electric cars
A Tesla Model S has a mass of 2350 kg (2.3 tonnes) with the largest (100 kWh) battery. Its range is claimed to be 315 miles. So the Model S is able to travel 315 miles/100 kWh = 3.15 miles per kWh.

Why do larger electric cars, with larger range, do fewer miles per kWh? The answer is simple. If you have a larger battery it’s much heavier (technically a larger mass). The Renault Zoe 52 kWh battery has a weight of 326 kg. The Tesla S 100 kWh battery has a weight of 625 kg, roughly twice that of the Renault Zoe for twice the capacity. If the battery has a larger mass then the whole car needs to have a larger mass because it needs to have larger motors to accelerate that mass, larger brakes to slow the mass down, stronger structures to support the mass, etc.

The biggest electric fuel tank on the market
So far as I am aware, the 100 kWh battery of the Tesla model S is the biggest car electrical fuel tank on the market. It has a capacity of 100 kWh.

Comparing electric car figures with a modern diesel car
Let’s compare the Tesla battery with the modest 47 litre fuel tank from my own medium-sized Renault Megane.
Diesel fuel has energy of 10 kWh per litre. So the the 47 litre tank has an energy capacity of 470 kWh. That sounds great until you realise that the efficiency of a diesel engine is about 30% compared with the near 100% efficiency of electrical motors. So let’s multiply by 30% (0.3) to work out the effective capacity of the Renault Megane fuel tank.
30% x 470 kWh = 141 kWh.
Gosh, that’s interesting. A medium-sized diesel car has nearly 50% more energy capacity than the largest electric car.
Moreover, since diesel has a density of about 0.8 kg per litre, the mass of the diesel tank plus the fuel will be about 47 kg for its energy capacity of 141 kWh, compared with the Tesla battery’s mass of 625 kg for an energy capacity of 100 kWh.
Diesel tank: 3 kWh/kg.
Electric battery: 0.16 kWh/kg.
The diesel fuel tank stores nearly 20 times as much per kilogram than the electric battery. In fact, for reasons I may tackle on a later post, the difference is even bigger than this.

Diesel car fuel consumption
The 2016 Renault Megane diesel is quiet, comfortable and has good economy figures.
It has a mass of 1500 kg, about the same smaller electric Zoe. (The Zoe’s mass is larger because the battery has a large mass.) Over around 8364 miles of mostly long-distance driving, it averaged 56 mpg with an average speed of about 30 mph. That’s a slower speed, and more accelerating and braking than the cars in the Carwow test.
8364 miles at 56 mpg is 8364/56 = 149.4 gallons for those 8364 miles.
Since there are 4.55 litres per gallon, that is 149.4 x 4.55 = 680 litre.
Each litre has 10 kWh of energy but diesel engines are only 30 % efficient, so we get 3 kWh of useful work out of each litre of diesel.
Total amount of useful work out = 3 kWh/litre x 680 litres = 2040 kWh for 8364 miles.
So energy needed per mile = 8364 miles/2040 kWh = 4.1 miles/kWh.
So we can see that the medium-sized Renault Megane travels as many miles per available kWh as a typical small electric car.

Broad facts worth remembering.
A small car will travel about 5 miles per kWh.
A large car will travel about 3 miles per kWh.
Medium cars, as you might imagine, are somewhere in the middle.
If you want to travel 300 miles in a large car, you need 100 kWh.
That is as simple as that.
A 50 kWh battery, powering a small car which does 5 miles/kWh, will give a range of 50 kWh x 5 miles/kWh = 250 miles, but there isn’t yet a small electrical car that will do that: the Renault Zoe, travelling at a constant speed along a motorway, only did 229 miles.

Other tests on the Megane
I did two trial runs on quiet motorways to measure fuel consumption at fixed speeds.
At 48 mph I averaged 72 mpg.
At 58 mph I averaged 58 mpg.
These figures point to the reasonableness of the overall 56 mpg figure experienced in practice.

What if?

What if coronavirus,
Creeps around unstoppably,
In aerosols too fine for masks to impede
And, like many a disease before it,
Is already so widespread
That, despite all our efforts,
It will take its toll
Whatever we do?

What if our many billions,
Poured out in lockdown
With no regard for wiser means,
Have had not the slightest effect,
Save for an impoverishment
That leads us to borrow more
From nations who hold in contempt
All we once regarded as dear?

What if men and women,
Entranced by man’s achievements,
With ne’er a thought for God,
Have grown oblivious to the powers of nature,
And, having been told so often
That we have rights to all and sundry,
Forget that the source is not government fiat
But fair winds and the sweat of man’s brow?

What if we are governed
By a godlessness
That, unlike the real Canute,
Knows not the limits of man’s power
But assures us that viruses can be beaten
And, were it politically expedient,
Would equally tell us
That the sea could be held back?

Canute the Great was king of Denmark, England and Norway. He was one of the first Scandinavian kings to accept Christianity. Medieval historian Norman Cantor called ‘the most effective king in Anglo-Saxon history‘, which corelates with the story of him demonstrating to his flattering courtiers that he had no power over the waves.

The story reminds one of Psalm 2:

Why do the nations conspire
    and the peoples plot in vain?
The kings of the earth rise up
    and the rulers band together
    against the Lord and against his anointed, saying,
“Let us break their chains
    and throw off their shackles.”

The One enthroned in heaven laughs;
    the Lord scoffs at them.
He rebukes them in his anger
    and terrifies them in his wrath, saying,
“I have installed my king
    on Zion, my holy mountain.”

I will proclaim the Lord’s decree:

He said to me, “You are my son;
    today I have become your father.
Ask me,
    and I will make the nations your inheritance,
    the ends of the earth your possession.
You will break them with a rod of iron;
    you will dash them to pieces like pottery.”

Therefore, you kings, be wise;
    be warned, you rulers of the earth.
Serve the Lord with fear
    and celebrate his rule with trembling.
Kiss his son, or he will be angry
    and your way will lead to your destruction,
for his wrath can flare up in a moment.
    Blessed are all who take refuge in him.

Abandoning mechanical disk drives

A fast mechanical hard drive, connected by a USB 3.0 connection to a laptop, conveys data at around 90 MB/s. Multiplying by 60 that’s 5400 MB/minute, ie around 200 minutes for 1 TB.

It is reasonable (at least in 2020) to say that man can survive on 1 TB, unless one is actively engaged in copious video editing, hence the many online storage systems that offer 1 TB as the entry level. If one does a complete backup monthly, not a daft thing to do, that means hanging around for 200 minutes, ie 3 or 4 hours, for a backup every month.

A fast 1TB USB solid state disk will operate many times faster than a mechanical hard drive. This one, from Sandisk, costs £150 and promises 1000 MB/s. In practice a typical laptop USB port will limit that to 400 MB/s. This is still five times as fast as a mechanical hard drive. It means completing a full backup in half an hour.

So moving from mechanical hard disks to fast solid-state-disks can save a couple of hours hanging around time per month.

If one regards one’s labour, or one’s free time, as worth as little as £5 per hour, swapping from a mechanical hard drive to SSD could save one 2 hours of hanging around per month, £10 per month, £120 per year…not far of the price of the fast SSD saved in a year. If one is in a commercial environment, the time value of money means that it is even more worthwhile to make the move to solid state storage.

Covid-19 and its overall effect on England and Wales death rate.

Covid-19 has affected death rates in obvious ways: it has been a direct cause of death; it has occurred alongside other illnesses, resulting in some earlier deaths as a consequence; its disruptive presence throughout the health service has resulted in early deaths for some who have been denied life-saving treatment, or have been reluctant to seek treatment, for other conditions. As 2020 comes to a close, we can see the overall effect of covid over getting on for a whole year and its overall impact on the death rate for England and Wales.

This graph shows the erratic nature of the weekly death figures. There are big spikes down at Christmas (and other holidays) when deaths are reported late and up just after New Year when the deaths over Christmas are added in. But this graph already shows some interesting figures.

The death rate for over 65s is about 4%. That means that 1 in 25 over-65s die within a year on average. But since there are about 11 million people over 65, that is about 440,000 over-65s deaths per year.

The death rate for under-65s is about 0.2%. We can see that that it has varied little as a result of covid. On average 1 in 500 under 65s die every year. And since there are nearly 50 million under-65s, that means that there are about 100,000 under-65s deaths per year.

The average total death rate for England and Wales is the 440,000 over-65s plus the 100,000 under-65s, giving a total annual death rate of about 540,000.

If we average the weekly death rate over a 4-week period, we see more of the underlying pattern.

This shows that the death rate for over 65s varies quite a lot over the year, hitting a peak sometimes over 6% in the winter, dropping to below 4% in summer. This year we had a very high peak of over 8% in March but that was followed by particularly low death rate in August. Some of those who died in the April covid peak did not live to die at their expected time of August. This provokes the question as to what extent the reduced deaths of August compensated for the increased deaths in May. To find out the extent of this balance, we average over a longer period of 4 months.

The 4-month average shows that 2020 is only a slightly unusual year. For the over-65s, the death rate rose to a high of 5.6%, while falling to an unusual low of 3.6% in September.

Certainly covid was instrumental in the particularly high death rate in April but there was another contributory factor: winter 2018-19 was a year in which there were relatively few flu deaths. This means that the vulnerable who would normally have died in that winter were still around in the peak of the 2019-20 season and among those who succumbed to covid.

We still see the particularly low death rate of 3.6% in September, a consequence of the vulnerable dying in April and not being around to contribute to the September statistics.

Monthly figures are not available for years before 2010. But whole year figures are available from 2006 and are shown here.

As can be seen, the 2020 death rate is entirely normal in the historical context, having an overall death rate for over 65s of 4.5%, slightly more than the peak of 4.4% in 2015 but less than the 4.8% figures from 2006 to 2008

Calculating total excess deaths
On the basis of previous years we predict how many deaths we would expect in a given year and compare it with the actual number of deaths. These figures we have been dealing with enable us to make a prediction for death rates for 2020.

If we confine our calculations to the recent low death-rate years, the average death rates for under-65s from 2013 week 52 to 2019 week 51 are as follows:
Under-65s – 0.169%
Over-65s – 4.321%

Using the figures below for the numbers in the two cohorts, this gives predicted deaths for 2020 of
Under-65s – 83,376
Over-65s – 459,545
Total – 562,922 (The extra 1 being a consequence of rounding issues.)

In fact the total deaths in England and Wales for 52 weeks from 2019 week 52 to 2020 week 51 has been 600,058. This is an excess death figure of 37,136. However, if we compare 2020 with 2006-8, we find that 2020 has had 27,491 fewer deaths pro rata than these years.

Even if the excess mortality in 2020 is close to 37,000, that includes deaths from all causes, including the knock-on excess deaths from all other diseases where treatment has been disrupted by attention to covid. (Many of us know perhaps more individuals who have had life-saving treatment disrupted than individuals who have died of covid.)

Bearing in mind that there have been suggestions that excess deaths for cancer may be, at a minimum, in the order of 10,000, it seems likely that the excess deaths due to covid will be well under 30,000. This is in stark contrast to the figure published for covid deaths in England and Wales of 65,795 (as on 31/12/2020).

As can be seen from the graph below about excess winter deaths, seasonal deaths commonly vary by over 20,000 from one year to another. In which case, even were the 37,000 excess deaths this year all due to covid, that would not be far out from the range of swings that habitually occur from year to year – see the graph below.

Survivability – the chance of surviving the year
So far we have calculated in terms of death rates, the chance of dying in a year. But a different, and possibly more relevant, perspective is to consider the chance of surviving the year, a more useful way of seeing the impact of covid on our lives.

For those of us over 65, over the 6 years from 2013 to 2019, the death rate was 4.3%, meaning that our chance of survival was 95.7%. 2019 was a particularly good year in which survivability of over-65s was 95.9%. In 2020, with a death rate of 4.5%, survival rate has been 95.5%.

Here we can see how survivability has changed over the last fifteen years.

With over-65s survival rate consistently a little above 95% we can see that the effect of covid has been really very small. We can stop worrying and regard 2020 as a normal year.

Since first publishing this, the Office for National Statistics has crunched the figures. Their figures are for the 12 months to the end of November 2020. Here is the graph for age-standardised-mortality.

As you can see, this graph is pretty much identical in shape to my own graph on death rates above. Again it shows that 2020 is not a particularly exceptional year.

The BBC, in their publication of the ONS statistics, were very naughty. They focused on the excess deaths in 2020 being greater than any other year since the Second World War. Well, since the population (at 68 million compared with 47 million during WW2) and the proportion of over-65s (18% as opposed to 10%) are greater in 2020 in any other year, of course we should expect the death rates to be greater.

Statistical notes
These figures are produced by taking the ONS published weekly death rate figures, multiplying them by 52 to give an annual death rate figure and dividing them by the numbers in the two cohorts (0-64 and 65+).

Numbers in the two cohorts are calculated from published UK population figures, reduced by 11.3% decreasing to 11.0% from 2010 to 2020 to account for those in Scotland and Northern Ireland.

Percentage of over-65s in the UK population is derived from the sources below, interpolating between fixed point data where necessary. Here are the figures used.